The paper is concerned with the lowest vibration modes of multi-component rods and cylinders with alternating high contrast material properties of the components. It is demonstrated that these modes correspond to almost rigid body motions of the “stiffer” components. A general perturbation scheme is developed. At leading order polynomial frequency equations are derived, along with linear algebraic equations for the associated eigenforms. In addition, for multi-component rods, higher order corrections are also obtained. Examples of three- and five-component structures are presented, illustrating the efficiency of the proposed approach.
COBISS.SI-ID: 1597174
Anti-plane dynamic shear of a strongly inhomogeneous dynamic laminate with traction-free faces is analysed. Two types of contrast are considered, including those for composite structures with thick or thin stiff outer layers. In both cases, the value of the cut-off frequency corresponding to the lowest antisymmetric vibration mode tends to zero. For this mode, the shortened dispersion relations and the associated formulae for displacement and stresses are obtained. The latter motivate the choice of appropriate settings, supporting the limiting forms of the original anti-plane problem. The asymptotic equation derived for a three-layered plate with thick faces is valid over the whole low-frequency range, whereas the range of validity of its counterpart for another type of contrast is restricted to a narrow vicinity of the cut-off frequency.
COBISS.SI-ID: 1593590
The edge bending wave on a thin isotropic semi-infinite plate reinforced by a beam is considered within the framework of the classical plate and beam theories. The boundary conditions at the plate edge incorporate both dynamic bending and twisting of the beam. A dispersion relation is derived along with its long-wave approximation. The effect of the problem parameters on the cutoffs of the wave in question is studied asymptotically. The obtained results are compared with calculations for the reinforcement in the form of a strip plate.
COBISS.SI-ID: 1693174